You don't wont lead, I think he is saying the rivets they use have some lead in them in order to be soft enough to properly form. The builders that have loose rivets are using to hard of a rivet like they use in fabrication where they heat the rivet then form it IMHO.

There are certain "leaded" steel alloys that (if memory serves!) lends itself to welding. I presume that in this application it will set easier, meaning less force required to set it. I think this is starting to split hairs as any "industrial" rivet will do the job.

Late to the party on this post, but I figured I'd share anyway.
Lead added to steel doesn't alloy with the steel, it forms small pockets or "inclusions" in the steel. It makes the steel easier to machine, with the lead acting like a lubricant to allow for faster cutting and smoother surfaces. What it doesn't do is make the steel any softer or easier to deform. For a better description see this site: Why Lead Is NOT An Alloying Element In Steel | Speaking of Precision Blog
So unless someone is buying steel with lead mixed in and making the rivets on a lathe, I doubt any rivet sets available are "leaded" steel, probably just plain old low carbon steel.